Mathematical Research Letters
Volume 15 (2008)
Totally geodesic subgraphs of the pants complex
Pages: 309 – 320
In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichmüller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extrinsic geometry of any $2$-dimensional stratum inside the Weil-Petersson completion.